Budapest has cracked down on short term rental regulations. They have to be registered, and that isn't an easy thing. As enforcement begins the quantity will reduce. Right now they aren't being required to post their registration numbers as in Paris, but I suspect that will change. I would ask before booking. One tip will be if they ask for your passport data, if not, they aren't operating legally. Doubt that a person renting an illegal flat will suffer any penalty, but always best to do business with honest folks.